## Sunday, September 20, 2020

### The Race of a Lifetime : Tadej POGAČAR's Stage 20 Time Trial Analysis

 Photo courtesy : Steephill.tv

Great comebacks are always a fascination for sports observers both from an entertainment and statistics perspective. Don't we all thrive for that moment when fortunes can be reversed and the underdog can win? In social psychology, this phenomenon even has a special name - schadenfreude.

Such a reversal in fortune happened during Stage 20 of the 36.2 km individual time trial at the Tour de France when a 21 year old Tadej Pogačar reclaimed nearly 2 minutes over his nearest rival Primoz Roglič, all but securing the title of the coveted yellow jersey and taking home 500,000 Euros in hard won prize money.

This was a rare feat to witness 20 days into the 3500 km Tour de France, and many had made up their minds that 57 seconds was a large chunk of time to win back from a highly motivated Primoz who had been in sitting in yellow for 11 days in a row. In the aftermath, the sport's pundits are going to be looking closely at how this was accomplished by the youngster, who beat just about every veteran of the time trial format available to contest that day.

Allow me to devote a brief section below to the analysis of the actual time trial performance and the corresponding power demands without going too much into the mathematics of it all. Please note this analysis remains to be validated since the official performance data from Team UAE Emirates is unavailable to the public as of today. Sources of my information are highlighted below and where required, educated guesses are employed. I also discuss my results towards the end of the article.

Assumptions & Considerations

I've used the following assumptions & considerations in this first order analysis :

• Weight/Height : 66 kg/176 cm (Source)
• Assumed Drag Area, CdA : T1/T2/T3/Finish = 0.22/0.24/0.3/0.3 sq.m (arbitrary but educated)
• Assumed Rolling Resistance Co-efficient, Crr : 0.002-0.0023, 25mm width (Vittoria Corsa tubeless)
• Assumed drivetrain efficiency : 98%
• Bike T1-T2 : TT bike w/ rim profile 60mm/Full Disc at 8.3 kg
• Bike T2-Finish : Road bike w/ rim profile 30mm/30mm at 6.8 kg (current UCI limit, source)
• Gear : Aerodynamic skin-suit and streamlined TT helmet
• Weather : Historical weather for 3-5pm local French time w/ winds 8.5-12 kph at 93-105 degrees range.
• Roads : Good (smooth asphalt) w/ mountainous terrain
• Course GPX source : Ritchie Porte's Strava data
• Performance time data : Pro Cycling Stats
• Model used : A widely cited & validated general purpose model of human power requirements in cycling
• Secondary power data for comparison : Thomas de Gendt's for Stage 20

Method

The race course was broken up into 4 segments corresponding to the official time checkpoints for the stage. A 1st order physics model was used in combination with official timings at those checkpoints to reverse calculate a suitable matching power output. I quote "suitable" as the numbers could change up or down depending on the actual conditions. From the potential locus of power outputs, this is a workable number for the rider, as I validate it below.

 Stage 20 ITT course profile

Results

The modeling indicates that for the first two sections totaling 30.3 km, the use of a special purpose TT bike weighing in at an assumed 8.3 kg and a body shape of CdA 0.22 sq.m required an average power output of 427 Watts. The results indicate a positive split with an average power of 451 Watts for the 1st segment until T1 and 402 Watts for the 2nd segment T1-T2.

In the vicinity of T2 at 30.3 km, a bike change happened where the TT bike was exchanged for a lighter road bike due to requirements necessitated by the gradient. This climb is at an average 8% gradient, kicking up to 20% in places. The bike change cost anywhere from 6-8 seconds in total, depending on how you start and stop the watch. This time cost is factored into the overall performance time.

Thus, in the last 5.9 km of this climb, the use of the assumed 6.8ckg road bike required an approximate average of 412 Watts at an estimated 6.2 W/kg (power to rider weight). The power demand for T2-T3 and T3-Finish of approximately 3.3 and 2.6 km each were 432 and 392 W (6.5 & 5.9 W/kg respectively).

The results are plotted in the image below :

 (Click to zoom) : Actual performance times along with corresponding modeled average power outputs for Tadej Pogacar in the final individual time trial of Stage 20 of the 2020 Tour de France.

Discussion

This is an unverified analysis done based on checkpoint timings obtained from and other publicly available information. An average power output of 419 Watts was required for this performance as per the modeling. What is definitely in question is the pacing profile over the course of time duration, which needs to be validated with real data.

Such a power output is not totally unrealistic for Tadej, given we know that in the 140km Mountain Stage on  Stage 8 of the Tour, he displayed a power output of 428 Watts over the Col de Peyresourde, climbing it in one of the fastest times recorded in recent history and an estimated power to weight ratio of over 6.5 W/kg. This was after 2 massive climbs before it and 120 km in the legs.

The modeled power output of 412W on the final 5.9 km climb equates to a power to weight ratio of 6.2 Watts/kg. Compare this to Thomas de Gendt's data from the same stage where he rode with an average of 405W at a power to weight of 5.9 Watts/kg. This is consistent with Thomas' performance data that shows he climbed 1:51 minutes slower than Tadej.

The overall data indicates a positive split of power across elapsed time duration. I justify this with two potentially valid points :

1. High motivation at the start, giving the rider the urge to ride hard in the first half. Tadej was in fact chasing what looked like an improbable target, a 58 second deficit to win the Tour de France. He might have purposely fired all cylinders, thus accounting for a potential loss of valuable seconds later during the bike change and any other unforeseen events on the climb.

2. The decrease in power output in the second half might be attributed to a combination of accumulated fatigue and/or a change of the power demand and the impact on feelings from a sudden change to a lighter bike on a steep climb. The "sudden" change to a new bike and the lack of objective power data from an absent head unit meant that Tadej had to guage his effort carefully. It could be that despite a drop in power and cadence, Tadej maintained the "same" or even "greater" level of perceived effort compared to previous flat sections of the course. However, this is just my speculation.

The choice of tire rolling resistances and drag areas although arbitrary, are not a totally wild guess. We know that Team UAE Emirates is sponsored by Vittoria in 2020, the tubeless varieties of which have reportedly exhibited some of the lowest rolling resistances at race speeds. Therefore, I have started off with an ideal case of 0.002 increasing this to 0.0023 at the climb. I figured the weaving on the climb at slow speeds combined with the quality of road on the gradient poses less than ideal conditions, justifying the small increase to Crr.

 Reported co-efficients of rolling resistance for some bicycle racing tires at race speeds. Source : Aerocoach

Professional TT riders are known to be slippery, exhibiting well under 0.25 sq.m of drag area in ideal conditions (smaller riders reportedly presenting less than 0.2 sq.m!) I have started off with an ideal scenario of 0.22 sq.m in the TT position due to Tadej's height and weight, increasing this to 0.3 sq.m on the climb which corresponds to a climbing position adopted with the hands on the hoods. Again, these numbers are arbitrarily chosen but there is no way at present to verify what the real numbers in open terrain might be. I do have some references from a Twitter conversation to believe that my choices are conservative for a top professional rider.

 CFD simulation results showing the individual contributions of wheels, bicycle and rider to CdA as well as the net CdA. Source : Fabio Malizia, Katholieke Universiteit, Leuven

The total system weight with rider and all accessories is an unknown. A premium TT bike setup of 8.3kg and lightweight road bike setup of 6.3kg are not unexpected and matches recorded observations on the internet.  However, the weight of his kit, shoes, helmet, bottle etc are unknowns. I have reasons to believe this will be under 1kg in total however the uncertainty in analysis from the final climb will stem from the uncertainty in system weight and rolling resistance. Regardless, the modeled power outputs are likely not very far off from the actual numbers.

Conclusion

I titled this race as the "race of a lifetime". Indeed, performances like these are hard to come by simply due to the immense difficulty of turning around such time advantages over a pile of fatigue and mental exhaustion 20 days into the Tour de France.

In some respects, Tadej's race performance has been likened to a pivotal moment in 1989 when the American Greg Lemond, bustling with energy and ready to try new technologies, beat the yellow jersey holder Laurent Fignon with the use of aerodynamic gear and in turn, winning the Tour de France.

Whether Tadej's victory was a matter of such marginal gains at the end of the day is debatable. Yes, two purpose made bikes were used in the time trial in an unusual manner, but this is increasingly becoming common in the top races these days. Moreover, unlike 1989, both Primoz and Tadej were arguably evenly matched in terms of technology, the funding and competent attention required to apply the technology. In fact, on race-day, they both undertook bike changes before the 6 km climb so any small variations in equipment came really down to supply differences from the equipment sponsors.

Did Tadej just ride his usual top race, as he does every time and was it Primoz who slowed and fizzled out? Well, I think that is clear to see. A race is indeed won by someone who slows the least. And what promoted this spectacular fall when the day demanded the best? Whether it was the massive pressure upon his Primoz's shoulders, or whether it was the failure of his power pacing model, or whether it was the fatigue, or ALL of the above, we will not know for sure.

What speaks to me from this performance is that marginal gains did not win, and something else contributed. Certainly Tadej rode the time trial of his life, and converted the opportunity of a lifetime to a magnificent victory. And I think in that moment, the individual qualities of what makes one rider better than another in the heat of the moment won. It really is a victory for the human element.

Years after his crushing defeat in the 1989 Tour, Laurent Fignon would write that despite getting over it, "you never stop grieving over an event like that; the best you can manage is to contain the effect it has on your mind." I hope that Primoz, as amazing a rider he has been to reach this level, is able to contain the effect of this race outcome on his mind and move on. He has more than a few good years of a top fight left in him at the very top. But an able and worthy opponent stands beside to check that in the form of Tadej Pogačar.